I was a postdoc in the Stanford math department for five years, from 1998 to 2003. I had a very pleasant time there, and had many pleasant interactions with my fellow department members; I’m glad that I ultimately left academia, but that’s purely because of me being a misfit.

Part of that being a misfit is that I didn’t spend nearly as much time as I should have actually doing math. I spent some of my time helping raise my daughter and playing video games (the latter not at work, of course; for the former, Miranda actually did hang out in my office a lot during the first two years of her life), and reading random books. I was still reading a fair amount of sociology of science books at the time; I dimly recall having fairly pleasant conversations about the topic with my fellow department members over lunch, but conversations with a modernist flavor that’s familiar to any reader of We Have Never Been Modern. This was fairly soon after the Sokal affair; that paper fit neatly into a narrative that was in the air, where mathematicians and hard scientists write papers full of gibberish that is incomprehensible to outsiders because that’s the only way to express our deep understanding of complex truths, while humanists and soft scientists write papers full of gibberish that is incomprehensible to outsiders in an attempt to cover up the vacuousness of what they’re saying. Those conversations weren’t generally mean, or as lacking in respect as I’m making them out to be here, but there was an asymmetry in the undertone.

The other thing that I spent a lot of time (far too much time, if you’re a postdoc in a research-focused school—teaching really isn’t what schools like Stanford are about) is thinking about teaching, which led to me running my courses in eccentric ways. The department was actually quite accepting of my eccentricity—I don’t know if anybody noticed the one time that I gave three quarters of my students an A in an intro course instead of weeding most of them out, but if anybody noticed, nobody brought it up to me—and while I was clearly an outlier within the department, my recollection was that I generally had pleasant conversations on teaching with other department members. (They were happy to let me stick around teaching calculus for a couple of years after my first postdoc expired, which I’m very grateful for.)

And there was a fair amount of surprisingly broad conversation about math teaching in the air. California had recently published a new set of standards (you can still see many of them on the California Content Standards page, look for the ones with the late-1990’s dates); and the math standards in particular had led to a fair amount of contention. I was curious about this (mostly because of my own interests, but also because they might be shaping the schools that my daughter would eventually enter), so I read through the various different standards; as I recall, the math standards seemed to me to be the most innocuous (standard skills-based stuff, noticeably but not offensively overstuffed), while the science ones were starting to get offensively overstuffed, the social studies were outright jingoistic, and if I wanted to design a curriculum to make somebody hate reading and writing, I’m not sure I could have done a better job than the English standards. Though maybe I’m being a bit hypocritical saying this, given my sniping above: I don’t have any expertise in childhood education, so I’m not the right person to criticize!

I think what was going on with the math standards was that they tapped into a real cultural discomfort with math teaching. The general context of the math wars was whether math teaching should focus on having kids be able to accurately carry out algorithms or whether they should focus on having kids develop a holistic understanding of concepts. Neither side thought that the other goal was bad: everybody would agree that algorithms should ideally lead to understanding of the concepts underlying them, while if you claim to have a holistic understanding of multiplication but can’t calculate seventeen times thirty-six, you’re just deluding yourself. But there was quite a lot of heat as to which side you could start on.

From my point of view, the heat was actually mostly in one direction: the algorithms folks were engaging in shameless fear-mongering about the conceptual approach. If I recall correctly, there was one local lady who went around to various local school board meetings telling people how, if their schools took a conceptual approach to teaching mathematics, then colleges wouldn’t accept their kids, which she based on some almost completely trumped-up claims about discussions with admissions departments. My take on this, on the other hand, was that the algorithms approach had been ruling the scene since basically forever, and it had a remarkable capacity for producing people who are actually traumatized by mathematics. That is not a term that I use lightly, and I recognize that, as forms of trauma go, math education trauma is relatively benign; it is, however, the case that, when I tell people that I’m a mathematician, the response is quite regularly for the person I’m speaking to to tell me unprompted how they’re a failure at mathematics. (With many variants; a quite common one is for people to say when they felt that they stopped being good at mathematics, e.g. “I was good at mathematics through calculus, but then linear algebra kicked my butt.”) I don’t believe any other field of study gets nearly the same tenor of response, and the situation is fucked up enough that, from the time I showed up in California until the time when Miranda was maybe in third grade, I actively avoided telling people I met outside of Stanford that I was a mathematician. (And of course now it doesn’t generally come up because I don’t work as a mathematician.) So, from my perspective, the results of the algorithmic approach towards teaching mathematics were Not Good, and it was high time to try something else.

The reason why I bring this up in a context of a discussion of the Stanford math department is that at least two members of the Stanford math department were involved in the production of the California state standards. My memory says three members, but when I look at the standard itself, the names that I recognize are James Milgram and Gunnar Carlsson, so I guess it was only two. The core of their involvement was before I showed up in the department (the standards have a 1997 date, and I was still in grad school then); and, in general, I think the idea of professional mathematicians being involved in the production of standards is a laudable idea, because they have specialized knowledge that will inform what is valuable for students to know, including subtle linkages between different areas.

It’s not, of course, the only specialized knowledge that is useful when writing a standard for teaching mathematics. I would like actual math teachers to be heavily involved in the production of such documents, as well as education professors who are up to date on the research for what educational approaches currently seem to give the best approach. And my impression (based admittedly on scanty evidence) is that this did not happen on the California math standards: that there was quite a lot of politicization in the composition of who participated in the committee and what voices were listened to, based on philosophical beliefs on what approach would work that weren’t supported by research.

I interacted with Gunnar Carlsson not infrequently during my time at Stanford (and worked part-time at a startup he cofounded during a few months when I wasn’t teaching), and all my memories of that interaction were pleasant: in particular, I’m sure his motives for devoting considerable amounts of time to the California math standards were public-spirited, trying to lend the help of his professional expertise without a particular didactic axe to grind. I spent much less time interacting with James Milgram; I’m sure his motives were also public-spirited, but I’m fairly sure that he did have an axe to grind, an axe that wasn’t backed up by his professional expertise.

Which brings us to the person whose name gives the title to this blog post, Jo Boaler. I assume we met during some sort of new faculty event in 1998; and we talked several times about math teaching over the years. I really enjoyed those conversations (and reading her first book), and found them very useful in thinking through some of the approaches I was trying to take in my course design. When I went further along that path, trying to turn what I was thinking about into an attempt to gather substantial data, she helped me with methodological advice and convinced a couple of her grad students to donate time to me interviewing some of the students who were taking my class. And I’m embarrassed that I didn’t do a real job of following through on that; though less embarrassed than I would be, because it was only by doing that that I started to realize just how much work it is to turn observations into real data that you can begin to draw conclusions from. (Mathematicians have it much easier in that respect in the relatively cut-and-dry nature of our proofs; though of course mathematics has its own significant difficulties because that cut-and-dried nature means that we’ve been able to dig very deep over the centuries into areas where our approach works.)

She mentioned conversations that she had had with Milgram. I dropped into his office once or twice because of that (and rarely ran into him in other contexts around the department, we traveled in different circles there); I don’t recall probing too deeply, but those conversations were consistent with Jo’s description of his behavior. I got the impression that my approach towards mathematics teaching was quite different to Milgram’s approach, that our opinions of mathematics teachers were also quite different, and that there wasn’t much point in having further conversations in that area.

I lost touch with Jo Boaler after my first three years at Stanford—she was busy, I was going in different directions. And of course, I’ve been out of academia for more than nine years by now. I was pleased to see her name show up recently in my twitter feed; I was sad to learn that the reason for that appearance was that she was starting a social media offensive campaign against Milgram (and Wayne Bishop, a math professor from elsewhere). According to Jo’s report of the situation, Milgram and Bishop have been trying to destroy her professional career; if a quarter of what Jo says there is accurate, then Milgram and Bishop’s behavior is, at the least, shameful.

Of course, I’m an outsider, so I can’t talk about the nuances of what happened first hand. But what Jo describes is consistent with what I saw: a strong ideological dislike for certain didactic approaches which translates into a lack of respect for people who aren’t aligned with scientists laying down the truth from high: a lack of respect for people who come to other conclusions, a lack of respect for professors who work in other fields, a lack of respect for people who are actually doing the day-to-day work of the teaching that is under discussion! There are strong structural undercurrents pulling in those directions in math departments all over the country (along with reinforcing undercurrents: Jo doesn’t call out gender issues in her web page, but they’re all over the place in science departments, and for that matter in Silicon Valley in general, as I’ve seen repeatedly in my post-Stanford career); a lot of the time, people work to fight those undercurrents and at least maintain a basic level of professional respect, but not always.

So: maybe Milgram and Bishop are right. But to believe that, I’ll have to believe that I should take the word of a couple of people who have never published peer-reviewed mathematics education research over somebody who has built a career on that, over the word of multiple departments that have given Jo Boaler research appointments over the years, over the word of a committee set up to investigate exactly that question. And you can make a consistent worldview out of that, if it’s the direction you choose to go in: it’s a world view that leads to statements like the one Bishop apparently made that schools of educations should be “nuked”. (That sort of lack of respect for math ed research by people who haven’t done any math ed research is depressingly common, though most people who hold such a view are more polite about it than that.)

It’s not a worldview that I hold, though. And I’m very glad Jo Boaler is showing the strength to fight against it.

16 Comments

“So: maybe Milgram and Bishop are right. But to believe that, I’ll have to believe that I should take the word of a couple of people who have never published peer-reviewed mathematics education research over somebody who has built a career on that, over the word of multiple departments that have given Jo Boaler research appointments over the years, over the word of a committee set up to investigate exactly that question.”

Getting a bit fed up with the idea that we can sort this out by arguing over who has the better credentials.

The fact is Milgram and Bishop have criticised Boaler’s research methods. None of these criticisms have been answered. Boaler has responded with accusations of persecution, an attempt to resurrect an ancient smear campaign and appeals to her personal authority and that of her supporters. You have also tried the last of these strategies.

If you know anything about how academic debate should work it’s pretty clear who can be taken seriously and who can’t.

Academic debate, at its core, happens in journals, conferences, citations, and the whole associated network of reputation that those are part of – it doesn’t happen because somebody publishes something out of left field and then complains that they’re not being listened to. This is as true in mathematics as it is in education research – mathematicians receive unsolicited proofs of unsolved conjectures or refutations of published work all of the time, and mathematicians call the people who write such letters ‘cranks’. Milgram has a better pedigree and a louder microphone than most cranks, but I don’t see why I should take his criticisms more seriously than Marilyn vos Savant’s criticisms of the proof of Fermat’s Last Theorem.

And really, “none of these criticisms have been answered”? What is the 2006 Stanford inquiry into Boaler’s research if it’s not an answer to those criticisms? And a particularly good answer, because that committee had access to Boaler’s research data, not simply the methods.

Firstly, I think you are out of date. There are a multitude of blogs and websites out there for academic work and discussion. There is simply no expectation that only peer-reviewed, published criticism of research is relevant and *certainly* no expectation that obviously flawed research should be acceepted as authoritative until an article about its flaws is published in a journal.

Secondly, maths education is hardly the exclusive preserve of professors of maths educations. If teachers and mathematicians are to be completely excluded from the discussion then why should either pay any attention to the research at all? Who is the research even for?

As for why you should take Milgram’s criticisms of Boaler’s works seriously, the main reason is because he appears to be right. Boaler’s refusal to engage with what are pretty straightforward points without personal attacks and claims of persecution hardly makes Milgram look like the crank. If she can find time to smear Bishop as a racist, and write website articles claiming persecution, it is odd that she cannot answer any actual points about her methodology.

If the 2006 “Stanford inquiry” has answered all criticisms of Boaler’s research then I would love to see it. However, all we know is that Stanford decided they would not take disciplinary action against her. “Not bad enough to get disciplined” is not the standard to which academic research should aspire and using that as evidence that the research is sound only emphasises the extent to which it cannot be defended as research.

Math teachers and professional mathematicians shouldn’t be excluded from the discussion of mathematics education; but the three fields have their own specific professional expertise, each field has areas where I’ll weight the opinions of practitioners more heavily than people in the other two fields.

From where I sit, it looks like Boaler has had to go farther than pretty much any academic than I can think of to respond to criticisms. (And criticisms about data that she can’t make publicly available, which puts her in an extra bind.) You’ve led off this comment thread by quoting my point of view on that matter; so I’m not surprised that we’re having a not-particularly convincing (in either direction) go-around on the matter, given that you pulled that quote out specifically as something you disagreed with.

I think this is where I sign out of the conversation – we’re reading the same words from different enough contexts that I don’t have the energy to try to make this productive conversation for either of us.

I’m not sure I follow. Milgram and Bishop may have acted out of ideological motivations. But they made several very specific charges, for example, that Boaler’s math test had incorrect questions, that her test was grades below the California standards, and that Railside’s students did not in fact take AP Calculus. It isn’t a matter of interpretation to point out that she hasn’t addressed those issues — she simply hasn’t, at least not that anyone can identify. Yet it would be easy to do so, if her research were defensible.

Don’t privacy regulations prevent her from addressing the last of these issues? I just looked at the Milgram/Bishop paper in question (at least what I assume is the paper in question, I see Clopton listed as another author, but it’s the first Google hit for ‘milgram bishop boaler’ and is on Milgram’s FTP site) to figure out whether the California standards issue is relevant, and I don’t even see a citation of the specific Boaler paper that they’re responding to. It’s probably buried somewhere in the pages (or maybe not – there’s no bibliography, I went through the 30-odd mentions of the word ‘Boaler’ in the article and I don’t see a mention of a paper), but I’m not reading Milgram’s paper in detail, skimming Boaler’s work to figure out which they’re referring to, and then reading the relevant bit of Boaler’s work in depth in an attempt to make sure I understand the context. (And an attempt I doubt I’d succeed in – in my experience, it’s quite hard for people outside the field to understand the context of publications in a professional journal.) I did look at a couple of the mistakes; I’m not impressed by those questions, but I don’t think they’re bad enough to invalidate the test by themselves (e.g. they don’t look like mistakes that would disproportionately favor students from a class with one teaching style over another), and published papers (in math as much as anywhere else) have minor mistakes all the time.

It is, of course, the case that if I wanted to seriously look into the claims in the Bishop/Clopton/Milgram paper, I would have to do quite a bit more legwork than this – probably many people reading this are rolling their eyes at my lack of enthusiasm for tracking down the details of claims. That is not how I choose to spend my time; spending half an evening writing up recollections is about my limit for this specific topic. I would be quite surprised, however, if the Stanford committee in question didn’t investigate those questions, and that’s a fair part of the point: I don’t see why I should spend many more evenings looking into this on the improbable chance that I’ll do a better job of understanding the nuances of the situation than people who have devoted years / decades of their life to that study. In other words: yes, she has addressed those issues, and done so in a fashion that’s more serious, more directly associated to her professional career, than almost any other academic has to go through.

And as to “it would be easy to do so, if her research were defensible” – I could just as easily say “it would be easy for Bishop, Milgram, and Clopton to get their paper published, if their research were defensible”. I don’t think either of those remarks would be entirely fair, but both sides seem to be choosing to play in battlegrounds where they’re most comfortable. So we have two asymmetric fights going on; my biases cause me to trust one the fight in one of those battlegrounds more than the other. Other people have different biases and come out on the other side.

I don’t follow the confidentiality point. Boaler writes an article saying that lots of Railside students took calculus and were achieving at a high level. Milgram/Clopton/Bishop review her article and say that Railside students did not, in fact, master calculus, as evidenced by two facts: 1) ZERO of them took the AP calculus test; and 2) most of them needed remediation when they got to college (according to a test scaled at a 7th grade level).

If the facts were on her side, Boaler could respond as follows: 1) MCB are wrong, because in fact x% of Railside students took the AP calculus test; 2) MCB are wrong, because only x% of Railside students needed remediation when they got to college. Those two sentences, if true, would be very simple to write.

Confidentiality can’t possibly be the reason that she is unable to defend her research on this point. If she can’t talk about how well Railside students were doing, she could never have written her article in the first place.

(By the way, MCB don’t need to publish their paper — mere reviews of other people’s papers generally don’t get published, yet still serve the critical function of reviewing the merits of someone else’s work.)

I don’t know how the confidentiality laws and agreements work; you could be right about that, but Boaler could also be legally or contractually bound from revealing more information. Hell, she just might not feel ethically right about that, given that she clearly has opponents who will dig into that information to try to remove confidentiality.

And, of course, MCB don’t need to publish their paper; they can do what they want. Similarly, I can choose whose help I want to evaluate their paper. In a normal context, I wouldn’t be nearly as stubborn as I’m being here; this is not a normal context, this is a context where thirteen years ago Milgram dissuaded Boaler from talking about her research, behaving in ways that I interpreted (both at the time and now) as disagreeing with the conclusions of her research rather than disagreeing with the content of her research. (Backed up with a healthy dose of contempt for math teachers.) That colors the way I see Milgram’s subsequent behavior, and the context in which I evaluate those subsequent claims. And in particular it means that I am not inclined to give him any benefit of the doubt when it comes to presenting Boaler’s research fairly (or any research on mathematical teaching styles); if he could convince a jury of her peers to take his claims seriously, then I’d be more willing to listen (though, honestly, I’d still be suspicious; quite possibly that’s a character flaw on my part); and, in fact, he did convince a jury of her peers to look into them, with the result that they’re siding with Boaler.

Who knows – maybe the jury of math ed bloggers will prove to be what matters. We certainly live in interesting times, where any significant scientific controversy gathers large numbers of people outside of the research community to argue both sides of the matter. Probably a good thing, in general; I’m still learning how to evaluate those controversies…

in fact, he did convince a jury of her peers to look into them, with the result that they’re siding with Boaler.

You’re talking about Stanford siding with Boaler in the sense that they weren’t willing to convict her of outright fraud and fire her. That doesn’t exonerate her research in the least bit from the claim that she is overselling her pet method of teaching.

More broadly, if math educators showed more signs of understanding the basic methods of research (i.e., how to do experiments competently), their opinions as peers would be more valuable.

For example, Boaler was doing school-level research — compute the intra-class correlation coefficient so as to come up with the true sample size? It doesn’t seem so; she treats the number of students as the sample size. And that is just wrong.

Worse, she designed her own test. This destroys her study’s credibility. Anyone familiar with education research knows how this stacks the deck — the test will almost certainly be written so as to match the teaching that is supposed to do “better.” That’s why it’s a pattern that anyone who evaluates their own program and designs their own test finds much greater effects than anyone else who has the least bit of independence.

They re-hired her, too. As to stacking the deck: my memory of reading Boaler’s original book (and it’s been over a decade since I’ve read it, I could be wrong) is that she tested students with tests that would favor an algorithmic, fact-drilling-based teaching style; this isn’t the style she would prefer, but using that as one of your evaluation methods sounds to me like a reasonable attempt to see what you might be losing with your teaching method as well as what you might be gaining.

Like the other guy said, the fact that Stanford hired her, or that she has good credentials, etc., is all a fallacious argument from authority. The fact still remains: people who know more about math and experimental design than her have listed several faults with her work, and her response is not to defend her work on the merits but to claim that she’s a Really Important Person who is being persecuted.

Another thing: Boaler says, “In 2003 Bishop discussed Schools of Education in the US and suggested to readers that they “nuke ‘em all dammit”. This, alongside his personal attacks on my work, prompted Stanford’s police department to travel to LA to speak to Wayne Bishop.”

“I recommended, perhaps facetiously, that a solution to the apparently insurmountable problems of schools of education would be to, “nuke ’em all, dammit.” For that offense, Dr. Boaler reported me as a potential terrorist to the Stanford University police (a faxed copy of her complaint was included in my defense package). Where had this come from? My post had been only to a “secure” education listserve so how had she obtained it to be able report me on March 3? Well Victor, of course . . . He was living on the listserve under the assumed personality of Rita Arrugio for exactly such purposes and passed my post along to Dr. Boaler who, in turn, supplied it to the Stanford campus police. That verification also helped with my defense.”

So according to that version of the story, it’s not as if the Stanford police themselves had, of their own accord, become upset about an obviously facetious comment Bishop had made on a private email list. What happened was that Boaler had an informant under a false identity on that list, and she then filed a false complaint about Bishop being a terrorist.

Note as well that earlier in that same post, Bishop points out that because he had made a skeptical comment to Education Week about Boaler’s research, Boaler tried to get his university’s ethics committee to censure him.

That puts the whole situation in rather a different light, and it looks as if Boaler has been the assailant as often as the victim.

I have been following this whole issue recently with interest. I am truly truly shocked to learn that Jo Boaler actually attempted to get someone that criticised her in trouble with the police – for terrorism…. Then she has the cheek to claim she is the one being harassed. This man had to put up with a police investigation having been accused by her of contemplating a heinous crime.
That she then fails to mention in her own list of complaints that the reason Bishop was investigated by the police was because she called them just seems par for the course for someone that can behave so unscrupulously . I am truly shocked by the revelation in these comments.

You folks are tag-teaming, right? I stop talking to Andrew, then JDE shows up; I don’t think I have anything more to add to that conversation, but he keeps the conversation going by bringing up something that I didn’t mention at all in my post. And then Hannah shows up to continue the conversation, acting surprised at this remarkable revalation JDE brought up, which she is “truly shocked” by.